Anisotropic materials, polarized

The analyzer is removed and the color of the sample is observed in plane-polarized light. If the sample is colored, the stage is rotated. Colored, anisotropic materials may show pleochroism—a change in color or hue when the orientation with respect to the vibration direction of the polarizer is changed. Any pleochroism should be noted and recorded. 

In practical PR experiments, the Ay 1) and y(2) in Eqs. (32) and (33) must be regarded as effective values, which are functions of the polarization of the probe beam, the symmetry of anisotropic materials, and the geometry of the experiments. 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

As demonstrated by the example of section 1.2.1, interaction of the electric field with anisotropic materials can cause its orthogonal components to have dissimilar phases and amplitudes. These properties of the electric vector describe the state of polarization of the electric vector. Since the electric vector lies in the plane perpendicular to the axis of propagation, a convenient description for this purpose is the two-component vector ... 

Imaging Anisotropic Materials with Polarized Radiation... 

For numerous questions related to the speciation of metal(loid) contaminants in natural and waste matrices, the combination of X-ray fluorescence, diffraction and absorption presented in this chapter offers a unique access to the problem. X-ray microscopy cannot compete with the atomic resolution offered by electron microscopy, but it offers a number of unique features. The chemical and structural information obtained by pSXRF and pSXRD can be used to identify the host solid phase by mapping the distributions of elements and solid species, respectively. Then the molecular-scale binding mechanism of trace elements by the host phase can be unraveled by pEXAFS spectroscopy. All these techniques can be applied with minimum preparation, minimizing any possible alteration of the sample. However, caution should be taken to not modify the initial form of the metal species by photon-assisted oxidation or reduction. This problem can be circumvented by decreasing the exposure time, photon density, or temperature. The polarization of the synchrotron radiation can be used to analyze anisotropic materials, which is important since many environmental minerals have a layered structure. 

Refractive index is dimensionless. For anisotropic materials the state of polarization of the light (and its direction, where appropriate) must be defined relative to a reference axis in the sample. It is then customary to quote two refractive indices additionally, the maximum difference between the two indices measured in two mutually perpendicular directions is termed the birefringence of the material. 

For an anisotropic material, I% Ieff becomes the modulus of an appropriate component of the tensor depending on the polarization... 

It should be noted, however, that the flexoelectric effect is not necessarily related to the ordering of molecular dipoles. Frost and Marcerou proposed another microscopic mechanism of the flexoelectric effect, which requires neither the asymmetry of the molecular shape nor the permanent molecular dipole. The macroscopic polarization may simply appear in the direction of the gradient of average density of the molecular quadrupole moments. The quadrupole mechanism of flexoelectricity is more general because, in principle, it should manifest itself in any anisotropic material with a non-zero quadrupole density including solid crystals d and elastomers. 

Chiral isotropic material (dissymmetric material) Achiral anisotropic material Chiral anisotropic material Left and right circularly polarized light Parallelly and perpendicularly linear polarized lighC Left and right elliptically polarized light... 

When linearly polarized light is incident on an anisotropic material that exhibits birefringence, the light propagates as two plane waves with orthogonal electric field vectors as shown in Figure 7.1.2. The electric field components Ex and Ey of these plane waves can be expressed as shown in Eq. 4 ... 

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